A tank is leaking at an increasing rate as indicated by the data below. Use the
ID: 2874351 • Letter: A
Question
A tank is leaking at an increasing rate as indicated by the data below. Use the table to answer the following questions.
Time (hr)
0
1
2
3
4
5
6
7
8
Leakage (gal/hr)
30
60
150
240
310
410
550
620
720
An upper limit estimate for the amount of material leaked (gal) after 4 hours is (???) gal.(Simplify)
A lower limit estimate for the amount of material leaked (gal) after 4 hours is (???) gal.(Simplify)
An upper limit estimate for the amount of material leaked (gal) after 8 hours is (???) gal.(Simplify)
A lower limit estimate for the amount of material leaked (gal) after 8 hours is (???) gal. (Simplify)
If the leakage occurs at a constant rate of 720 gal/hr after 8 hours and the tank initially held
22,000 gallons of material, an estimate for the least amount of time for the tank to empty is (???) hr.
(Round to the Nearest tenth)
If the leakage occurs at a constant rate of 720 gal/hr after 8 hours and the tank initially held
22,000 gallons of material, an estimate for the most amount of time for the tank to empty is (???) hr.
(Round to the nearest tenth.)
Time (hr)
0
1
2
3
4
5
6
7
8
Leakage (gal/hr)
30
60
150
240
310
410
550
620
720
Explanation / Answer
From the given question,
Time (hr)
0
1
2
3
4
5
6
7
8
Leakage (gal/hr)
30
60
150
240
310
410
550
620
720
1.An upper limit estimate for the amount of material leaked (gal) after 4 hours is
=(60+150+240+310)*1
=760 gal
2.A lower limit estimate for the amount of material leaked (gal) after 4 hours is
=(30+60+150+240)*1
=480 gal
3.An upper limit estimate for the amount of material leaked (gal) after 8 hours is
=(60+150+240+310+410+550+620+720)*1
=3060 gal
4.A lower limit estimate for the amount of material leaked (gal) after 8 hours is
=(30+60+150+240+310+410+550+620)*1
=2370 gal
5. Total material= 22000 gal
To get least time, we will take upper limit estimate after 8 hrs=3060 gal
total material left= 22000-3060=18,940 gal
leaking rate=720 gal/hr
time needed to empty = 18,940/720=26.3 hrs
Total time needed to empty= 26.3+8=34.3 hrs
6.Total material= 22000 gal
To get maximum time, we will take lower limit estimate after 8 hrs=2370 gal
total material left= 22000-2370=19,630 gal
leaking rate=720 gal/hr
time needed to empty = 19,630/720=27.2 hrs
Total time needed to empty= 27.2.3+8=35.2 hrs
Time (hr)
0
1
2
3
4
5
6
7
8
Leakage (gal/hr)
30
60
150
240
310
410
550
620
720
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